Actual source code: snesncg.c
1: #include <../src/snes/impls/ncg/snesncgimpl.h>
2: const char *const SNESNCGTypes[] = {"FR","PRP","HS","DY","CD","SNESNCGType","SNES_NCG_",NULL};
4: static PetscErrorCode SNESReset_NCG(SNES snes)
5: {
6: return 0;
7: }
9: /*
10: SNESDestroy_NCG - Destroys the private SNES_NCG context that was created with SNESCreate_NCG().
12: Input Parameter:
13: . snes - the SNES context
15: Application Interface Routine: SNESDestroy()
16: */
17: static PetscErrorCode SNESDestroy_NCG(SNES snes)
18: {
19: PetscFree(snes->data);
20: return 0;
21: }
23: /*
24: SNESSetUp_NCG - Sets up the internal data structures for the later use
25: of the SNESNCG nonlinear solver.
27: Input Parameters:
28: + snes - the SNES context
29: - x - the solution vector
31: Application Interface Routine: SNESSetUp()
32: */
34: static PetscErrorCode SNESSetUp_NCG(SNES snes)
35: {
36: SNESSetWorkVecs(snes,2);
38: if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
39: return 0;
40: }
42: static PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
43: {
44: PetscScalar alpha, ptAp;
45: Vec X, Y, F, W;
46: SNES snes;
47: PetscReal *fnorm, *xnorm, *ynorm;
49: SNESLineSearchGetSNES(linesearch, &snes);
50: X = linesearch->vec_sol;
51: W = linesearch->vec_sol_new;
52: F = linesearch->vec_func;
53: Y = linesearch->vec_update;
54: fnorm = &linesearch->fnorm;
55: xnorm = &linesearch->xnorm;
56: ynorm = &linesearch->ynorm;
58: if (!snes->jacobian) {
59: SNESSetUpMatrices(snes);
60: }
62: /*
64: The exact step size for unpreconditioned linear CG is just:
65: alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
66: */
67: SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre);
68: VecDot(F, F, &alpha);
69: MatMult(snes->jacobian, Y, W);
70: VecDot(Y, W, &ptAp);
71: alpha = alpha / ptAp;
72: VecAXPY(X,-alpha,Y);
73: SNESComputeFunction(snes,X,F);
75: VecNorm(F,NORM_2,fnorm);
76: VecNorm(X,NORM_2,xnorm);
77: VecNorm(Y,NORM_2,ynorm);
78: return 0;
79: }
81: /*MC
82: SNESLINESEARCHNCGLINEAR - Special line search only for SNESNCG
84: This line search uses the length "as if" the problem is linear (that is what is computed by the linear CG method) using the Jacobian of the function.
85: alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy) where r (f) is the current residual (function value), p (y) is the current search direction.
87: Notes: This requires a Jacobian-vector product but does not require the solution of a linear system with the Jacobian
89: This is a "odd-ball" line search, we don't know if it is in the literature or used in practice by anyone.
91: Level: advanced
93: .seealso: SNESLineSearchCreate(), SNESLineSearchSetType()
94: M*/
96: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
97: {
98: linesearch->ops->apply = SNESLineSearchApply_NCGLinear;
99: linesearch->ops->destroy = NULL;
100: linesearch->ops->setfromoptions = NULL;
101: linesearch->ops->reset = NULL;
102: linesearch->ops->view = NULL;
103: linesearch->ops->setup = NULL;
104: return 0;
105: }
107: /*
108: SNESSetFromOptions_NCG - Sets various parameters for the SNESNCG method.
110: Input Parameter:
111: . snes - the SNES context
113: Application Interface Routine: SNESSetFromOptions()
114: */
115: static PetscErrorCode SNESSetFromOptions_NCG(PetscOptionItems *PetscOptionsObject,SNES snes)
116: {
117: SNES_NCG *ncg = (SNES_NCG*)snes->data;
118: PetscBool debug = PETSC_FALSE;
119: SNESNCGType ncgtype=ncg->type;
120: SNESLineSearch linesearch;
122: PetscOptionsHead(PetscOptionsObject,"SNES NCG options");
123: PetscOptionsBool("-snes_ncg_monitor","Monitor the beta values used in the NCG iterations","SNES",ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL);
124: if (debug) {
125: ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
126: }
127: PetscOptionsEnum("-snes_ncg_type","NCG Beta type used","SNESNCGSetType",SNESNCGTypes,(PetscEnum)ncg->type,(PetscEnum*)&ncgtype,NULL);
128: SNESNCGSetType(snes, ncgtype);
129: PetscOptionsTail();
130: if (!snes->linesearch) {
131: SNESGetLineSearch(snes, &linesearch);
132: if (!((PetscObject)linesearch)->type_name) {
133: if (!snes->npc) {
134: SNESLineSearchSetType(linesearch, SNESLINESEARCHCP);
135: } else {
136: SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);
137: }
138: }
139: }
140: return 0;
141: }
143: /*
144: SNESView_NCG - Prints info from the SNESNCG data structure.
146: Input Parameters:
147: + SNES - the SNES context
148: - viewer - visualization context
150: Application Interface Routine: SNESView()
151: */
152: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
153: {
154: SNES_NCG *ncg = (SNES_NCG *) snes->data;
155: PetscBool iascii;
157: PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
158: if (iascii) {
159: PetscViewerASCIIPrintf(viewer, " type: %s\n", SNESNCGTypes[ncg->type]);
160: }
161: return 0;
162: }
164: /*
166: Assuming F = SNESComputeFunction(X) compute Y^tJ^tF using a simple secant approximation of the jacobian.
168: This routine is not currently used. I don't know what its intended purpose is.
170: Note it has a hardwired differencing parameter of 1e-5
172: */
173: PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar * ytJtf)
174: {
175: PetscScalar ftf, ftg, fty, h;
177: VecDot(F, F, &ftf);
178: VecDot(F, Y, &fty);
179: h = 1e-5*fty / fty;
180: VecCopy(X, W);
181: VecAXPY(W, -h, Y); /* this is arbitrary */
182: SNESComputeFunction(snes, W, G);
183: VecDot(G, F, &ftg);
184: *ytJtf = (ftg - ftf) / h;
185: return 0;
186: }
188: /*@
189: SNESNCGSetType - Sets the conjugate update type for SNESNCG.
191: Logically Collective on SNES
193: Input Parameters:
194: + snes - the iterative context
195: - btype - update type
197: Options Database:
198: . -snes_ncg_type <prp,fr,hs,dy,cd> -strategy for selecting algorithm for computing beta
200: Level: intermediate
202: SNESNCGSelectTypes:
203: + SNES_NCG_FR - Fletcher-Reeves update
204: . SNES_NCG_PRP - Polak-Ribiere-Polyak update
205: . SNES_NCG_HS - Hestenes-Steifel update
206: . SNES_NCG_DY - Dai-Yuan update
207: - SNES_NCG_CD - Conjugate Descent update
209: Notes:
210: SNES_NCG_PRP is the default, and the only one that tolerates generalized search directions.
212: It is not clear what "generalized search directions" means, does it mean use with a nonlinear preconditioner,
213: that is using -npc_snes_type <type>, SNESSetNPC(), or SNESGetNPC()?
215: @*/
216: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
217: {
219: PetscTryMethod(snes,"SNESNCGSetType_C",(SNES,SNESNCGType),(snes,btype));
220: return 0;
221: }
223: static PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
224: {
225: SNES_NCG *ncg = (SNES_NCG*)snes->data;
227: ncg->type = btype;
228: return 0;
229: }
231: /*
232: SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.
234: Input Parameters:
235: . snes - the SNES context
237: Output Parameter:
238: . outits - number of iterations until termination
240: Application Interface Routine: SNESSolve()
241: */
242: static PetscErrorCode SNESSolve_NCG(SNES snes)
243: {
244: SNES_NCG *ncg = (SNES_NCG*)snes->data;
245: Vec X,dX,lX,F,dXold;
246: PetscReal fnorm, ynorm, xnorm, beta = 0.0;
247: PetscScalar dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
248: PetscInt maxits, i;
249: SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
250: SNESLineSearch linesearch;
251: SNESConvergedReason reason;
255: PetscCitationsRegister(SNESCitation,&SNEScite);
256: snes->reason = SNES_CONVERGED_ITERATING;
258: maxits = snes->max_its; /* maximum number of iterations */
259: X = snes->vec_sol; /* X^n */
260: dXold = snes->work[0]; /* The previous iterate of X */
261: dX = snes->work[1]; /* the preconditioned direction */
262: lX = snes->vec_sol_update; /* the conjugate direction */
263: F = snes->vec_func; /* residual vector */
265: SNESGetLineSearch(snes, &linesearch);
267: PetscObjectSAWsTakeAccess((PetscObject)snes);
268: snes->iter = 0;
269: snes->norm = 0.;
270: PetscObjectSAWsGrantAccess((PetscObject)snes);
272: /* compute the initial function and preconditioned update dX */
274: if (snes->npc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
275: SNESApplyNPC(snes,X,NULL,dX);
276: SNESGetConvergedReason(snes->npc,&reason);
277: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
278: snes->reason = SNES_DIVERGED_INNER;
279: return 0;
280: }
281: VecCopy(dX,F);
282: VecNorm(F,NORM_2,&fnorm);
283: } else {
284: if (!snes->vec_func_init_set) {
285: SNESComputeFunction(snes,X,F);
286: } else snes->vec_func_init_set = PETSC_FALSE;
288: /* convergence test */
289: VecNorm(F,NORM_2,&fnorm);
290: SNESCheckFunctionNorm(snes,fnorm);
291: VecCopy(F,dX);
292: }
293: if (snes->npc) {
294: if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
295: SNESApplyNPC(snes,X,F,dX);
296: SNESGetConvergedReason(snes->npc,&reason);
297: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
298: snes->reason = SNES_DIVERGED_INNER;
299: return 0;
300: }
301: }
302: }
303: VecCopy(dX,lX);
304: VecDot(dX, dX, &dXdotdX);
306: PetscObjectSAWsTakeAccess((PetscObject)snes);
307: snes->norm = fnorm;
308: PetscObjectSAWsGrantAccess((PetscObject)snes);
309: SNESLogConvergenceHistory(snes,fnorm,0);
310: SNESMonitor(snes,0,fnorm);
312: /* test convergence */
313: (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
314: if (snes->reason) return 0;
316: /* Call general purpose update function */
317: if (snes->ops->update) {
318: (*snes->ops->update)(snes, snes->iter);
319: }
321: /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */
323: for (i = 1; i < maxits + 1; i++) {
324: /* some update types require the old update direction or conjugate direction */
325: if (ncg->type != SNES_NCG_FR) {
326: VecCopy(dX, dXold);
327: }
328: SNESLineSearchApply(linesearch,X,F,&fnorm,lX);
329: SNESLineSearchGetReason(linesearch, &lsresult);
330: SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
331: if (lsresult) {
332: if (++snes->numFailures >= snes->maxFailures) {
333: snes->reason = SNES_DIVERGED_LINE_SEARCH;
334: return 0;
335: }
336: }
337: if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
338: snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
339: return 0;
340: }
341: /* Monitor convergence */
342: PetscObjectSAWsTakeAccess((PetscObject)snes);
343: snes->iter = i;
344: snes->norm = fnorm;
345: snes->xnorm = xnorm;
346: snes->ynorm = ynorm;
347: PetscObjectSAWsGrantAccess((PetscObject)snes);
348: SNESLogConvergenceHistory(snes,snes->norm,0);
349: SNESMonitor(snes,snes->iter,snes->norm);
351: /* Test for convergence */
352: (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
353: if (snes->reason) return 0;
355: /* Call general purpose update function */
356: if (snes->ops->update) {
357: (*snes->ops->update)(snes, snes->iter);
358: }
359: if (snes->npc) {
360: if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
361: SNESApplyNPC(snes,X,NULL,dX);
362: SNESGetConvergedReason(snes->npc,&reason);
363: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
364: snes->reason = SNES_DIVERGED_INNER;
365: return 0;
366: }
367: VecCopy(dX,F);
368: } else {
369: SNESApplyNPC(snes,X,F,dX);
370: SNESGetConvergedReason(snes->npc,&reason);
371: if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
372: snes->reason = SNES_DIVERGED_INNER;
373: return 0;
374: }
375: }
376: } else {
377: VecCopy(F,dX);
378: }
380: /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
381: switch (ncg->type) {
382: case SNES_NCG_FR: /* Fletcher-Reeves */
383: dXolddotdXold= dXdotdX;
384: VecDot(dX, dX, &dXdotdX);
385: beta = PetscRealPart(dXdotdX / dXolddotdXold);
386: break;
387: case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
388: dXolddotdXold= dXdotdX;
389: VecDotBegin(dX, dX, &dXdotdXold);
390: VecDotBegin(dXold, dX, &dXdotdXold);
391: VecDotEnd(dX, dX, &dXdotdX);
392: VecDotEnd(dXold, dX, &dXdotdXold);
393: beta = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
394: if (beta < 0.0) beta = 0.0; /* restart */
395: break;
396: case SNES_NCG_HS: /* Hestenes-Stiefel */
397: VecDotBegin(dX, dX, &dXdotdX);
398: VecDotBegin(dX, dXold, &dXdotdXold);
399: VecDotBegin(lX, dX, &lXdotdX);
400: VecDotBegin(lX, dXold, &lXdotdXold);
401: VecDotEnd(dX, dX, &dXdotdX);
402: VecDotEnd(dX, dXold, &dXdotdXold);
403: VecDotEnd(lX, dX, &lXdotdX);
404: VecDotEnd(lX, dXold, &lXdotdXold);
405: beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
406: break;
407: case SNES_NCG_DY: /* Dai-Yuan */
408: VecDotBegin(dX, dX, &dXdotdX);
409: VecDotBegin(lX, dX, &lXdotdX);
410: VecDotBegin(lX, dXold, &lXdotdXold);
411: VecDotEnd(dX, dX, &dXdotdX);
412: VecDotEnd(lX, dX, &lXdotdX);
413: VecDotEnd(lX, dXold, &lXdotdXold);
414: beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
415: break;
416: case SNES_NCG_CD: /* Conjugate Descent */
417: VecDotBegin(dX, dX, &dXdotdX);
418: VecDotBegin(lX, dXold, &lXdotdXold);
419: VecDotEnd(dX, dX, &dXdotdX);
420: VecDotEnd(lX, dXold, &lXdotdXold);
421: beta = PetscRealPart(dXdotdX / lXdotdXold);
422: break;
423: }
424: if (ncg->monitor) {
425: PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta);
426: }
427: VecAYPX(lX, beta, dX);
428: }
429: PetscInfo(snes, "Maximum number of iterations has been reached: %D\n", maxits);
430: if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
431: return 0;
432: }
434: /*MC
435: SNESNCG - Nonlinear Conjugate-Gradient method for the solution of general nonlinear systems.
437: Level: beginner
439: Options Database:
440: + -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
441: . -snes_linesearch_type <cp,l2,basic> - Line search type.
442: - -snes_ncg_monitor - Print the beta values used in the ncg iteration, .
444: Notes:
445: This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
446: gradient method. This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
447: chooses the initial search direction as F(x) for the initial guess x.
449: Only supports left non-linear preconditioning.
451: Default line search is SNESLINESEARCHCP, unless a nonlinear preconditioner is used with -npc_snes_type <type>, SNESSetNPC(), or SNESGetNPC() then
452: SNESLINESEARCHL2 is used. Also supports the special purpose line search SNESLINESEARCHNCGLINEAR
454: References:
455: . * - Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
456: SIAM Review, 57(4), 2015
458: .seealso: SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNEWTONTR, SNESNGMRES, SNESQN, SNESLINESEARCHNCGLINEAR, SNESNCGSetType(), SNESNCGGetType(), SNESLineSearchSetType()
459: M*/
460: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
461: {
462: SNES_NCG * neP;
464: snes->ops->destroy = SNESDestroy_NCG;
465: snes->ops->setup = SNESSetUp_NCG;
466: snes->ops->setfromoptions = SNESSetFromOptions_NCG;
467: snes->ops->view = SNESView_NCG;
468: snes->ops->solve = SNESSolve_NCG;
469: snes->ops->reset = SNESReset_NCG;
471: snes->usesksp = PETSC_FALSE;
472: snes->usesnpc = PETSC_TRUE;
473: snes->npcside = PC_LEFT;
475: snes->alwayscomputesfinalresidual = PETSC_TRUE;
477: if (!snes->tolerancesset) {
478: snes->max_funcs = 30000;
479: snes->max_its = 10000;
480: snes->stol = 1e-20;
481: }
483: PetscNewLog(snes,&neP);
484: snes->data = (void*) neP;
485: neP->monitor = NULL;
486: neP->type = SNES_NCG_PRP;
487: PetscObjectComposeFunction((PetscObject)snes,"SNESNCGSetType_C", SNESNCGSetType_NCG);
488: return 0;
489: }